If I understand your intention right, I don't expect, that mixing/adding the microphone signals from multiple rooms and locations serves the purpose. It will reduce overall signal-to-noise ratio by a considerable factor and possibly causing failure of a system, that works well with a single microphone.
For reliable operation, you would want to implement a kind of squelch or noise-gate functionality, that only activates a microphone channel above a certain sound level, or a mux that selects the channel with highest sound level. There may be still a problem if arbitrary interfering sound sources are present in a room.